/export/starexec/sandbox/solver/bin/starexec_run_Transition /export/starexec/sandbox/benchmark/theBenchmark.smt2 /export/starexec/sandbox/output/output_files


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YES

DP problem for innermost termination.
P =
  f8#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) -> f4#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) 
  f5#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f2#(I0, I1, I2, -1 + I3, rnd5, I17, I6, I7, I8, 1 + I8, I10, I11, I12, I13, I14, rnd16, 0, I17, I18, I19, I4, I21, I22, I23, I24) [0 <= I3 /\ 0 <= I8 /\ y1 = I23 /\ rnd5 = y1 /\ rnd16 = rnd16]
  f2#(I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f5#(I76, I77, I78, I79, I80, I81, I82, I83, I85, I85, I86, I87, I88, I101, I102, I91, I92, I96, I94, I95, I96, I97, I98, I99, I100) [0 <= I79 /\ 0 <= I85 /\ I103 = I103 /\ I104 = I104 /\ 0 <= I103 - I104 /\ I101 = I101 /\ I102 = I102 /\ I92 <= 0 /\ 0 <= I92]
  f4#(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f1#(I105, I106, I107, I108, I109, I110, rnd7, rnd8, I113, I114, rnd11, 17, I117, I118, I119, I120, I121, I123, I123, I124, I125, I126, I127, I128, I129) [I130 = 0 /\ I131 = 0 /\ I132 = 0 /\ rnd11 = I132 /\ 0 <= -1 - I132 + 17 /\ rnd7 = rnd7 /\ rnd8 = 1 + I132]
  f3#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157) -> f1#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157) 
  f1#(I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f3#(I158, I159, I160, I161, I162, I163, I183, 1 + I165, I166, I167, 1 + I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182) [I183 = I183 /\ 0 <= -1 - I165 + I169 /\ 0 <= I168]
  f1#(I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f2#(I190, I185, -2 + I194, -1 + I185 + -2 + I194, I209, I210, I190, I191, I192, 1, I194, I195, I196, I211, I212, I213, 0, rnd18, I202, I203, rnd21, I205, I206, I207, I208) [0 <= I194 /\ -1 * I191 + I195 <= 0 /\ 0 <= I194 /\ 0 <= I194 /\ y15 = I190 /\ I214 = y15 /\ y16 = 0 /\ 0 <= I194 /\ y18 = I214 /\ y8 = I208 /\ I215 = y8 /\ y9 = y9 /\ y4 = y16 /\ y13 = 0 /\ 0 <= -1 + I194 /\ y4 <= 0 /\ 0 <= y4 /\ y13 <= 0 /\ 0 <= y13 /\ y17 = y18 /\ 0 <= -1 + I194 /\ y19 = I215 /\ y10 = I203 /\ I216 = y10 /\ y11 = y11 /\ y5 = y17 /\ y14 = 0 /\ 0 <= -2 + I194 /\ y6 = y6 /\ y7 = y7 /\ 0 <= y6 - y7 /\ I211 = I211 /\ I212 = I212 /\ y14 <= 0 /\ 0 <= y14 /\ rnd18 = y19 /\ 0 <= -2 + I194 /\ rnd21 = I216 /\ y12 = I205 /\ I209 = y12 /\ I213 = I213 /\ I210 = rnd18]
R = 
  f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) -> f4(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) 
  f5(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f2(I0, I1, I2, -1 + I3, rnd5, I17, I6, I7, I8, 1 + I8, I10, I11, I12, I13, I14, rnd16, 0, I17, I18, I19, I4, I21, I22, I23, I24) [0 <= I3 /\ 0 <= I8 /\ y1 = I23 /\ rnd5 = y1 /\ rnd16 = rnd16]
  f5(I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f7(rnd1, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) [rnd1 = rnd1 /\ 0 <= I29 /\ I29 <= 0 /\ 0 <= I33 /\ 0 <= I28]
  f2(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f6(I50, I51, I52, I53, I54, rnd6, I56, I57, I58, I59, I60, I61, rnd13, rnd14, rnd15, I65, I55, I67, I68, I69, I70, I71, I72, I73, I74) [0 <= I53 /\ 0 <= I59 /\ y2 = y2 /\ y3 = y3 /\ 1 + y2 - y3 <= 0 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ I75 = I72 /\ rnd6 = I75 /\ rnd13 = rnd13 /\ 0 <= I53 /\ 0 <= -1 + I59]
  f2(I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f5(I76, I77, I78, I79, I80, I81, I82, I83, I85, I85, I86, I87, I88, I101, I102, I91, I92, I96, I94, I95, I96, I97, I98, I99, I100) [0 <= I79 /\ 0 <= I85 /\ I103 = I103 /\ I104 = I104 /\ 0 <= I103 - I104 /\ I101 = I101 /\ I102 = I102 /\ I92 <= 0 /\ 0 <= I92]
  f4(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f1(I105, I106, I107, I108, I109, I110, rnd7, rnd8, I113, I114, rnd11, 17, I117, I118, I119, I120, I121, I123, I123, I124, I125, I126, I127, I128, I129) [I130 = 0 /\ I131 = 0 /\ I132 = 0 /\ rnd11 = I132 /\ 0 <= -1 - I132 + 17 /\ rnd7 = rnd7 /\ rnd8 = 1 + I132]
  f3(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157) -> f1(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157) 
  f1(I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f3(I158, I159, I160, I161, I162, I163, I183, 1 + I165, I166, I167, 1 + I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182) [I183 = I183 /\ 0 <= -1 - I165 + I169 /\ 0 <= I168]
  f1(I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f2(I190, I185, -2 + I194, -1 + I185 + -2 + I194, I209, I210, I190, I191, I192, 1, I194, I195, I196, I211, I212, I213, 0, rnd18, I202, I203, rnd21, I205, I206, I207, I208) [0 <= I194 /\ -1 * I191 + I195 <= 0 /\ 0 <= I194 /\ 0 <= I194 /\ y15 = I190 /\ I214 = y15 /\ y16 = 0 /\ 0 <= I194 /\ y18 = I214 /\ y8 = I208 /\ I215 = y8 /\ y9 = y9 /\ y4 = y16 /\ y13 = 0 /\ 0 <= -1 + I194 /\ y4 <= 0 /\ 0 <= y4 /\ y13 <= 0 /\ 0 <= y13 /\ y17 = y18 /\ 0 <= -1 + I194 /\ y19 = I215 /\ y10 = I203 /\ I216 = y10 /\ y11 = y11 /\ y5 = y17 /\ y14 = 0 /\ 0 <= -2 + I194 /\ y6 = y6 /\ y7 = y7 /\ 0 <= y6 - y7 /\ I211 = I211 /\ I212 = I212 /\ y14 <= 0 /\ 0 <= y14 /\ rnd18 = y19 /\ 0 <= -2 + I194 /\ rnd21 = I216 /\ y12 = I205 /\ I209 = y12 /\ I213 = I213 /\ I210 = rnd18]

The dependency graph for this problem is:
  0 -> 3
  1 -> 2
  2 -> 1
  3 -> 5
  4 -> 5, 6
  5 -> 4
  6 -> 2
Where:
  0) f8#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) -> f4#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) 
  1) f5#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f2#(I0, I1, I2, -1 + I3, rnd5, I17, I6, I7, I8, 1 + I8, I10, I11, I12, I13, I14, rnd16, 0, I17, I18, I19, I4, I21, I22, I23, I24) [0 <= I3 /\ 0 <= I8 /\ y1 = I23 /\ rnd5 = y1 /\ rnd16 = rnd16]
  2) f2#(I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f5#(I76, I77, I78, I79, I80, I81, I82, I83, I85, I85, I86, I87, I88, I101, I102, I91, I92, I96, I94, I95, I96, I97, I98, I99, I100) [0 <= I79 /\ 0 <= I85 /\ I103 = I103 /\ I104 = I104 /\ 0 <= I103 - I104 /\ I101 = I101 /\ I102 = I102 /\ I92 <= 0 /\ 0 <= I92]
  3) f4#(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f1#(I105, I106, I107, I108, I109, I110, rnd7, rnd8, I113, I114, rnd11, 17, I117, I118, I119, I120, I121, I123, I123, I124, I125, I126, I127, I128, I129) [I130 = 0 /\ I131 = 0 /\ I132 = 0 /\ rnd11 = I132 /\ 0 <= -1 - I132 + 17 /\ rnd7 = rnd7 /\ rnd8 = 1 + I132]
  4) f3#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157) -> f1#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157) 
  5) f1#(I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f3#(I158, I159, I160, I161, I162, I163, I183, 1 + I165, I166, I167, 1 + I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182) [I183 = I183 /\ 0 <= -1 - I165 + I169 /\ 0 <= I168]
  6) f1#(I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f2#(I190, I185, -2 + I194, -1 + I185 + -2 + I194, I209, I210, I190, I191, I192, 1, I194, I195, I196, I211, I212, I213, 0, rnd18, I202, I203, rnd21, I205, I206, I207, I208) [0 <= I194 /\ -1 * I191 + I195 <= 0 /\ 0 <= I194 /\ 0 <= I194 /\ y15 = I190 /\ I214 = y15 /\ y16 = 0 /\ 0 <= I194 /\ y18 = I214 /\ y8 = I208 /\ I215 = y8 /\ y9 = y9 /\ y4 = y16 /\ y13 = 0 /\ 0 <= -1 + I194 /\ y4 <= 0 /\ 0 <= y4 /\ y13 <= 0 /\ 0 <= y13 /\ y17 = y18 /\ 0 <= -1 + I194 /\ y19 = I215 /\ y10 = I203 /\ I216 = y10 /\ y11 = y11 /\ y5 = y17 /\ y14 = 0 /\ 0 <= -2 + I194 /\ y6 = y6 /\ y7 = y7 /\ 0 <= y6 - y7 /\ I211 = I211 /\ I212 = I212 /\ y14 <= 0 /\ 0 <= y14 /\ rnd18 = y19 /\ 0 <= -2 + I194 /\ rnd21 = I216 /\ y12 = I205 /\ I209 = y12 /\ I213 = I213 /\ I210 = rnd18]

We have the following SCCs.
  { 4, 5 }
  { 1, 2 }

DP problem for innermost termination.
P =
  f5#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f2#(I0, I1, I2, -1 + I3, rnd5, I17, I6, I7, I8, 1 + I8, I10, I11, I12, I13, I14, rnd16, 0, I17, I18, I19, I4, I21, I22, I23, I24) [0 <= I3 /\ 0 <= I8 /\ y1 = I23 /\ rnd5 = y1 /\ rnd16 = rnd16]
  f2#(I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f5#(I76, I77, I78, I79, I80, I81, I82, I83, I85, I85, I86, I87, I88, I101, I102, I91, I92, I96, I94, I95, I96, I97, I98, I99, I100) [0 <= I79 /\ 0 <= I85 /\ I103 = I103 /\ I104 = I104 /\ 0 <= I103 - I104 /\ I101 = I101 /\ I102 = I102 /\ I92 <= 0 /\ 0 <= I92]
R = 
  f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) -> f4(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) 
  f5(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f2(I0, I1, I2, -1 + I3, rnd5, I17, I6, I7, I8, 1 + I8, I10, I11, I12, I13, I14, rnd16, 0, I17, I18, I19, I4, I21, I22, I23, I24) [0 <= I3 /\ 0 <= I8 /\ y1 = I23 /\ rnd5 = y1 /\ rnd16 = rnd16]
  f5(I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f7(rnd1, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) [rnd1 = rnd1 /\ 0 <= I29 /\ I29 <= 0 /\ 0 <= I33 /\ 0 <= I28]
  f2(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f6(I50, I51, I52, I53, I54, rnd6, I56, I57, I58, I59, I60, I61, rnd13, rnd14, rnd15, I65, I55, I67, I68, I69, I70, I71, I72, I73, I74) [0 <= I53 /\ 0 <= I59 /\ y2 = y2 /\ y3 = y3 /\ 1 + y2 - y3 <= 0 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ I75 = I72 /\ rnd6 = I75 /\ rnd13 = rnd13 /\ 0 <= I53 /\ 0 <= -1 + I59]
  f2(I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f5(I76, I77, I78, I79, I80, I81, I82, I83, I85, I85, I86, I87, I88, I101, I102, I91, I92, I96, I94, I95, I96, I97, I98, I99, I100) [0 <= I79 /\ 0 <= I85 /\ I103 = I103 /\ I104 = I104 /\ 0 <= I103 - I104 /\ I101 = I101 /\ I102 = I102 /\ I92 <= 0 /\ 0 <= I92]
  f4(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f1(I105, I106, I107, I108, I109, I110, rnd7, rnd8, I113, I114, rnd11, 17, I117, I118, I119, I120, I121, I123, I123, I124, I125, I126, I127, I128, I129) [I130 = 0 /\ I131 = 0 /\ I132 = 0 /\ rnd11 = I132 /\ 0 <= -1 - I132 + 17 /\ rnd7 = rnd7 /\ rnd8 = 1 + I132]
  f3(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157) -> f1(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157) 
  f1(I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f3(I158, I159, I160, I161, I162, I163, I183, 1 + I165, I166, I167, 1 + I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182) [I183 = I183 /\ 0 <= -1 - I165 + I169 /\ 0 <= I168]
  f1(I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f2(I190, I185, -2 + I194, -1 + I185 + -2 + I194, I209, I210, I190, I191, I192, 1, I194, I195, I196, I211, I212, I213, 0, rnd18, I202, I203, rnd21, I205, I206, I207, I208) [0 <= I194 /\ -1 * I191 + I195 <= 0 /\ 0 <= I194 /\ 0 <= I194 /\ y15 = I190 /\ I214 = y15 /\ y16 = 0 /\ 0 <= I194 /\ y18 = I214 /\ y8 = I208 /\ I215 = y8 /\ y9 = y9 /\ y4 = y16 /\ y13 = 0 /\ 0 <= -1 + I194 /\ y4 <= 0 /\ 0 <= y4 /\ y13 <= 0 /\ 0 <= y13 /\ y17 = y18 /\ 0 <= -1 + I194 /\ y19 = I215 /\ y10 = I203 /\ I216 = y10 /\ y11 = y11 /\ y5 = y17 /\ y14 = 0 /\ 0 <= -2 + I194 /\ y6 = y6 /\ y7 = y7 /\ 0 <= y6 - y7 /\ I211 = I211 /\ I212 = I212 /\ y14 <= 0 /\ 0 <= y14 /\ rnd18 = y19 /\ 0 <= -2 + I194 /\ rnd21 = I216 /\ y12 = I205 /\ I209 = y12 /\ I213 = I213 /\ I210 = rnd18]

We use the basic value criterion with the projection function NU:
  NU[f2#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22,z23,z24,z25)] = z4
  NU[f5#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22,z23,z24,z25)] = z4

This gives the following inequalities:
  0 <= I3 /\ 0 <= I8 /\ y1 = I23 /\ rnd5 = y1 /\ rnd16 = rnd16  ==>  I3 >! -1 + I3
  0 <= I79 /\ 0 <= I85 /\ I103 = I103 /\ I104 = I104 /\ 0 <= I103 - I104 /\ I101 = I101 /\ I102 = I102 /\ I92 <= 0 /\ 0 <= I92  ==>  I79 (>! \union =) I79

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f2#(I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f5#(I76, I77, I78, I79, I80, I81, I82, I83, I85, I85, I86, I87, I88, I101, I102, I91, I92, I96, I94, I95, I96, I97, I98, I99, I100) [0 <= I79 /\ 0 <= I85 /\ I103 = I103 /\ I104 = I104 /\ 0 <= I103 - I104 /\ I101 = I101 /\ I102 = I102 /\ I92 <= 0 /\ 0 <= I92]
R = 
  f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) -> f4(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) 
  f5(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f2(I0, I1, I2, -1 + I3, rnd5, I17, I6, I7, I8, 1 + I8, I10, I11, I12, I13, I14, rnd16, 0, I17, I18, I19, I4, I21, I22, I23, I24) [0 <= I3 /\ 0 <= I8 /\ y1 = I23 /\ rnd5 = y1 /\ rnd16 = rnd16]
  f5(I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f7(rnd1, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) [rnd1 = rnd1 /\ 0 <= I29 /\ I29 <= 0 /\ 0 <= I33 /\ 0 <= I28]
  f2(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f6(I50, I51, I52, I53, I54, rnd6, I56, I57, I58, I59, I60, I61, rnd13, rnd14, rnd15, I65, I55, I67, I68, I69, I70, I71, I72, I73, I74) [0 <= I53 /\ 0 <= I59 /\ y2 = y2 /\ y3 = y3 /\ 1 + y2 - y3 <= 0 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ I75 = I72 /\ rnd6 = I75 /\ rnd13 = rnd13 /\ 0 <= I53 /\ 0 <= -1 + I59]
  f2(I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f5(I76, I77, I78, I79, I80, I81, I82, I83, I85, I85, I86, I87, I88, I101, I102, I91, I92, I96, I94, I95, I96, I97, I98, I99, I100) [0 <= I79 /\ 0 <= I85 /\ I103 = I103 /\ I104 = I104 /\ 0 <= I103 - I104 /\ I101 = I101 /\ I102 = I102 /\ I92 <= 0 /\ 0 <= I92]
  f4(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f1(I105, I106, I107, I108, I109, I110, rnd7, rnd8, I113, I114, rnd11, 17, I117, I118, I119, I120, I121, I123, I123, I124, I125, I126, I127, I128, I129) [I130 = 0 /\ I131 = 0 /\ I132 = 0 /\ rnd11 = I132 /\ 0 <= -1 - I132 + 17 /\ rnd7 = rnd7 /\ rnd8 = 1 + I132]
  f3(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157) -> f1(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157) 
  f1(I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f3(I158, I159, I160, I161, I162, I163, I183, 1 + I165, I166, I167, 1 + I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182) [I183 = I183 /\ 0 <= -1 - I165 + I169 /\ 0 <= I168]
  f1(I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f2(I190, I185, -2 + I194, -1 + I185 + -2 + I194, I209, I210, I190, I191, I192, 1, I194, I195, I196, I211, I212, I213, 0, rnd18, I202, I203, rnd21, I205, I206, I207, I208) [0 <= I194 /\ -1 * I191 + I195 <= 0 /\ 0 <= I194 /\ 0 <= I194 /\ y15 = I190 /\ I214 = y15 /\ y16 = 0 /\ 0 <= I194 /\ y18 = I214 /\ y8 = I208 /\ I215 = y8 /\ y9 = y9 /\ y4 = y16 /\ y13 = 0 /\ 0 <= -1 + I194 /\ y4 <= 0 /\ 0 <= y4 /\ y13 <= 0 /\ 0 <= y13 /\ y17 = y18 /\ 0 <= -1 + I194 /\ y19 = I215 /\ y10 = I203 /\ I216 = y10 /\ y11 = y11 /\ y5 = y17 /\ y14 = 0 /\ 0 <= -2 + I194 /\ y6 = y6 /\ y7 = y7 /\ 0 <= y6 - y7 /\ I211 = I211 /\ I212 = I212 /\ y14 <= 0 /\ 0 <= y14 /\ rnd18 = y19 /\ 0 <= -2 + I194 /\ rnd21 = I216 /\ y12 = I205 /\ I209 = y12 /\ I213 = I213 /\ I210 = rnd18]

The dependency graph for this problem is:
  2 -> 
Where:
  2) f2#(I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f5#(I76, I77, I78, I79, I80, I81, I82, I83, I85, I85, I86, I87, I88, I101, I102, I91, I92, I96, I94, I95, I96, I97, I98, I99, I100) [0 <= I79 /\ 0 <= I85 /\ I103 = I103 /\ I104 = I104 /\ 0 <= I103 - I104 /\ I101 = I101 /\ I102 = I102 /\ I92 <= 0 /\ 0 <= I92]

We have the following SCCs.
  

DP problem for innermost termination.
P =
  f3#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157) -> f1#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157) 
  f1#(I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f3#(I158, I159, I160, I161, I162, I163, I183, 1 + I165, I166, I167, 1 + I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182) [I183 = I183 /\ 0 <= -1 - I165 + I169 /\ 0 <= I168]
R = 
  f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) -> f4(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) 
  f5(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f2(I0, I1, I2, -1 + I3, rnd5, I17, I6, I7, I8, 1 + I8, I10, I11, I12, I13, I14, rnd16, 0, I17, I18, I19, I4, I21, I22, I23, I24) [0 <= I3 /\ 0 <= I8 /\ y1 = I23 /\ rnd5 = y1 /\ rnd16 = rnd16]
  f5(I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f7(rnd1, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) [rnd1 = rnd1 /\ 0 <= I29 /\ I29 <= 0 /\ 0 <= I33 /\ 0 <= I28]
  f2(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f6(I50, I51, I52, I53, I54, rnd6, I56, I57, I58, I59, I60, I61, rnd13, rnd14, rnd15, I65, I55, I67, I68, I69, I70, I71, I72, I73, I74) [0 <= I53 /\ 0 <= I59 /\ y2 = y2 /\ y3 = y3 /\ 1 + y2 - y3 <= 0 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ I75 = I72 /\ rnd6 = I75 /\ rnd13 = rnd13 /\ 0 <= I53 /\ 0 <= -1 + I59]
  f2(I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f5(I76, I77, I78, I79, I80, I81, I82, I83, I85, I85, I86, I87, I88, I101, I102, I91, I92, I96, I94, I95, I96, I97, I98, I99, I100) [0 <= I79 /\ 0 <= I85 /\ I103 = I103 /\ I104 = I104 /\ 0 <= I103 - I104 /\ I101 = I101 /\ I102 = I102 /\ I92 <= 0 /\ 0 <= I92]
  f4(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f1(I105, I106, I107, I108, I109, I110, rnd7, rnd8, I113, I114, rnd11, 17, I117, I118, I119, I120, I121, I123, I123, I124, I125, I126, I127, I128, I129) [I130 = 0 /\ I131 = 0 /\ I132 = 0 /\ rnd11 = I132 /\ 0 <= -1 - I132 + 17 /\ rnd7 = rnd7 /\ rnd8 = 1 + I132]
  f3(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157) -> f1(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157) 
  f1(I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f3(I158, I159, I160, I161, I162, I163, I183, 1 + I165, I166, I167, 1 + I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182) [I183 = I183 /\ 0 <= -1 - I165 + I169 /\ 0 <= I168]
  f1(I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f2(I190, I185, -2 + I194, -1 + I185 + -2 + I194, I209, I210, I190, I191, I192, 1, I194, I195, I196, I211, I212, I213, 0, rnd18, I202, I203, rnd21, I205, I206, I207, I208) [0 <= I194 /\ -1 * I191 + I195 <= 0 /\ 0 <= I194 /\ 0 <= I194 /\ y15 = I190 /\ I214 = y15 /\ y16 = 0 /\ 0 <= I194 /\ y18 = I214 /\ y8 = I208 /\ I215 = y8 /\ y9 = y9 /\ y4 = y16 /\ y13 = 0 /\ 0 <= -1 + I194 /\ y4 <= 0 /\ 0 <= y4 /\ y13 <= 0 /\ 0 <= y13 /\ y17 = y18 /\ 0 <= -1 + I194 /\ y19 = I215 /\ y10 = I203 /\ I216 = y10 /\ y11 = y11 /\ y5 = y17 /\ y14 = 0 /\ 0 <= -2 + I194 /\ y6 = y6 /\ y7 = y7 /\ 0 <= y6 - y7 /\ I211 = I211 /\ I212 = I212 /\ y14 <= 0 /\ 0 <= y14 /\ rnd18 = y19 /\ 0 <= -2 + I194 /\ rnd21 = I216 /\ y12 = I205 /\ I209 = y12 /\ I213 = I213 /\ I210 = rnd18]

We use the reverse value criterion with the projection function NU:
  NU[f1#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22,z23,z24,z25)] = -1 - z8 + z12 + -1 * 0
  NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22,z23,z24,z25)] = -1 - z8 + z12 + -1 * 0

This gives the following inequalities:
    ==>  -1 - I140 + I144 + -1 * 0 >= -1 - I140 + I144 + -1 * 0
  I183 = I183 /\ 0 <= -1 - I165 + I169 /\ 0 <= I168  ==>  -1 - I165 + I169 + -1 * 0 > -1 - (1 + I165) + I169 + -1 * 0  with  -1 - I165 + I169 + -1 * 0 >= 0

We remove all the strictly oriented dependency pairs.

DP problem for innermost termination.
P =
  f3#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157) -> f1#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157) 
R = 
  f8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) -> f4(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) 
  f5(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f2(I0, I1, I2, -1 + I3, rnd5, I17, I6, I7, I8, 1 + I8, I10, I11, I12, I13, I14, rnd16, 0, I17, I18, I19, I4, I21, I22, I23, I24) [0 <= I3 /\ 0 <= I8 /\ y1 = I23 /\ rnd5 = y1 /\ rnd16 = rnd16]
  f5(I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) -> f7(rnd1, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49) [rnd1 = rnd1 /\ 0 <= I29 /\ I29 <= 0 /\ 0 <= I33 /\ 0 <= I28]
  f2(I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f6(I50, I51, I52, I53, I54, rnd6, I56, I57, I58, I59, I60, I61, rnd13, rnd14, rnd15, I65, I55, I67, I68, I69, I70, I71, I72, I73, I74) [0 <= I53 /\ 0 <= I59 /\ y2 = y2 /\ y3 = y3 /\ 1 + y2 - y3 <= 0 /\ rnd14 = rnd14 /\ rnd15 = rnd15 /\ I75 = I72 /\ rnd6 = I75 /\ rnd13 = rnd13 /\ 0 <= I53 /\ 0 <= -1 + I59]
  f2(I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100) -> f5(I76, I77, I78, I79, I80, I81, I82, I83, I85, I85, I86, I87, I88, I101, I102, I91, I92, I96, I94, I95, I96, I97, I98, I99, I100) [0 <= I79 /\ 0 <= I85 /\ I103 = I103 /\ I104 = I104 /\ 0 <= I103 - I104 /\ I101 = I101 /\ I102 = I102 /\ I92 <= 0 /\ 0 <= I92]
  f4(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f1(I105, I106, I107, I108, I109, I110, rnd7, rnd8, I113, I114, rnd11, 17, I117, I118, I119, I120, I121, I123, I123, I124, I125, I126, I127, I128, I129) [I130 = 0 /\ I131 = 0 /\ I132 = 0 /\ rnd11 = I132 /\ 0 <= -1 - I132 + 17 /\ rnd7 = rnd7 /\ rnd8 = 1 + I132]
  f3(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157) -> f1(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157) 
  f1(I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f3(I158, I159, I160, I161, I162, I163, I183, 1 + I165, I166, I167, 1 + I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181, I182) [I183 = I183 /\ 0 <= -1 - I165 + I169 /\ 0 <= I168]
  f1(I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f2(I190, I185, -2 + I194, -1 + I185 + -2 + I194, I209, I210, I190, I191, I192, 1, I194, I195, I196, I211, I212, I213, 0, rnd18, I202, I203, rnd21, I205, I206, I207, I208) [0 <= I194 /\ -1 * I191 + I195 <= 0 /\ 0 <= I194 /\ 0 <= I194 /\ y15 = I190 /\ I214 = y15 /\ y16 = 0 /\ 0 <= I194 /\ y18 = I214 /\ y8 = I208 /\ I215 = y8 /\ y9 = y9 /\ y4 = y16 /\ y13 = 0 /\ 0 <= -1 + I194 /\ y4 <= 0 /\ 0 <= y4 /\ y13 <= 0 /\ 0 <= y13 /\ y17 = y18 /\ 0 <= -1 + I194 /\ y19 = I215 /\ y10 = I203 /\ I216 = y10 /\ y11 = y11 /\ y5 = y17 /\ y14 = 0 /\ 0 <= -2 + I194 /\ y6 = y6 /\ y7 = y7 /\ 0 <= y6 - y7 /\ I211 = I211 /\ I212 = I212 /\ y14 <= 0 /\ 0 <= y14 /\ rnd18 = y19 /\ 0 <= -2 + I194 /\ rnd21 = I216 /\ y12 = I205 /\ I209 = y12 /\ I213 = I213 /\ I210 = rnd18]

The dependency graph for this problem is:
  4 -> 
Where:
  4) f3#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157) -> f1#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157) 

We have the following SCCs.